Re: [computer-go] taking advantage of board symmetries in neuralnetworks

[matth1@xxxxxxxxxxxxxx]

I agree that the cuplrit sounds like your mofification to the errors. I think I know what you mean by taking the average error and there is a sort of logic to it. The problem is that you are essentially destroying information and creating over successive generations a filtering effect. The result would be similar to that of reducing the number of active nodes. I was using neural nets for 9x9 Go about 10 years ago. Only I was using forward edelmann training, a variation of genetic algorithms (This had worked in Othello, so I thought it would be a useful way to attack 9x9 go, though results were poor.

Matt


>  from:    Thomas Johnson <thomas@xxxxxxxxxxxxxxxxx>
>  date:    Thu, 18 Dec 2003 00:21:40
>  to:      computer-go@xxxxxxxxxxxxxxxxx
>  subject: Re: [computer-go] taking advantage of board symmetries in neural networks
> 
> It sounds like your modification of the backprop algorithm might be the
> culprit. I don't completely understand what you mean by taking the
> average error of similar nodes, but if you're doing something like
> averaging the error of your network at each of the four corners, that's
> going to mess stuff up. 
> 
> One alternative way to take advantage of board symmetries might be to
> use each board position to generate four training cases per board
> position (one for each board rotation). This doesn't use the inherent
> structure of the network per se, but it should help the network learn
> more rapidly from fewer board positions. 
> 
> Tom
> 
> On Wed, 2003-12-17 at 13:17, Frank Steinmann wrote:
> > I'm having some experience with a neural network at the moment. My network
> > (for 9x9 go) has three fully connected 9x9 layers (so each node of the
> > hidden layer has 81 inputs and 81 outputs). For my experiments, I'm using
> > random-players, which make any legal moves (except for moving into their own
> > eyes) as long as possible.
> > 
> > First thing I'm trying to learn is the board evaluation at the end of a
> > game, black territory (only eyes in this case) gets value 1, white territory
> > gets value -1, occupied intersections get value 0. Of course that's easy to
> > do without a neural network, but I want to keep it simple at the beginning.
> > 
> > In my first experiment, I initialized the weights with random values and let
> > the network learn from a few hundred end positions, using the back
> > propagation algorithm. After that, the nework performed quite well
> > (performance could have been better but there was a tendency towards the
> > correct results).
> > 
> > After that I thought about taking advantage of the board symmetries, so I
> > initialized the weights of similar connections (according to the symmetries)
> > with equal values. To maintain the equality of the weights during the
> > learning process it was necessary to modify the back propagation algorithm.
> > I took the error of similar nodes, computed the average error, and replaced
> > the errors of these nodes by the average error. This caused similar
> > connections to keep equal weights.
> > The results after learning from a few hundred bad were bad. The network
> > didn't seem to learn at all. Maybe the average error was not convenient, so
> > I tried the same thing using the largest error of similar nodes instead of
> > the average error, but results weren't better.
> > 
> > So my question is how to take advantage of the board symmetries here?
> > Apparently my approach didn't lead to the desired success. Does anyone have
> > any experience with that? I'm sure you have... ;)
> > 
> > Frank
> > 
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> -- 
> Thomas Johnson <thomas@xxxxxxxxxxxxxxxxx>
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